Celtic's two strikers delivered the goals that knocked Stranraer out of the Scottish Cup in a composed display.
Leigh Griffiths struck once in each half, and almost scored a third with a remarkable volley.
Carlton Cole headed his first goal for Celtic in between, as the duo showed signs of a developing partnership.
Stranraer worked hard, but made little headway in front of goal as the gulf between the League One side and the Premiership champions was laid bare.
Ronny Deila's team selection set the tone for Celtic's display. There was no sense of the visitors using the tie as an opportunity to bring fringe players to the fore, and the performance was shaped by its professionalism and attitude.
Inevitably, it was Celtic's greater quality that separated the teams. Stranraer were industrious, working tirelessly to close down space. In possession, though, they could not create anything meaningful, whereas Celtic were at their most alert in the final third.
Although Cole was occasionally sluggish in his movement, his power and wiliness provided Celtic with a presence to play off up front. Even in a strong wind, and on a bobbly pitch, the visitors took command.
The breakthrough came when Callum McGregor saw the opportunity to slip Griffiths through, and the weight of his pass was perfect. The striker weighed up his options and expertly placed a shot beyond Max Currie.
The teenage Stranraer goalkeeper was helpless on that occasion, but he was impressively resolute moments later as he saved twice from Griffiths in a matter of seconds. Celtic's intent was evident, and there was reward for that endeavour before half-time, when Cole headed Nir Bitton's cross in from close range.
There was less coherence to Celtic's attacking play after the break, which allowed Stranraer a sense that the game was not over as a contest. Even so, Currie had to be alert. A jinking run by Stefan Johansen ended with his shot being cleared off the line by Scott Robertson, then Cole's overhead kick was held in a diving save by Currie.
As if not wanting to be outdone by his strike partner, Griffiths unleashed an outstanding acrobatic volley, flipping in mid air to send the ball over his shoulder and on target, but Currie tipped his effort over the bar.
Stranraer remained subdued as an attacking force, although Craig Malcolm's header from inside the six-yard box forced the Celtic goalkeeper Logan Bailly to dive on the ball. In contrast, when Griffiths was sent through by an excellent Scott Allan pass, the striker finished decisively.
Celtic will be satisfied with this display, but the behaviour of some away fans - smoke-bombs were evident before and during the game - will have caused them some dismay.
Full Time Match ends, Stranraer 0, Celtic 3.
90:00 +2:02 Full timeFull Time Second Half ends, Stranraer 0, Celtic 3.
90:00 +1:05Attempt missed. Scott Allan (Celtic) right footed shot from outside the box is close, but misses to the left.
90:00 +0:23Attempt missed. Tomas Rogic (Celtic) right footed shot from outside the box is close, but misses to the right.
85:37Corner, Celtic. Conceded by Max Currie.
85:31Attempt saved. Leigh Griffiths (Celtic) left footed shot from outside the box is saved in the bottom left corner.
83:57 Goal scoredGoal! Goal! Stranraer 0, Celtic 3. Leigh Griffiths (Celtic) left footed shot from the centre of the box to the bottom left corner. Assisted by Scott Allan.
82:45Foul by Liam Dick (Stranraer).
82:45Callum McGregor (Celtic) wins a free kick in the defensive half.
82:34Attempt saved. Scott Allan (Celtic) right footed shot from the centre of the box is saved in the bottom right corner.
81:22Corner, Celtic. Conceded by Steven Bell.
80:30Attempt saved. Leigh Griffiths (Celtic) right footed shot from the right side of the box is saved in the bottom left corner.
79:41 SubstitutionSubstitution Substitution, Stranraer. Ryan Thomson replaces Jamie Longworth.
76:52Attempt saved. Jamie Longworth (Stranraer) header from the centre of the box is saved in the centre of the goal.
76:32Corner, Stranraer. Conceded by Stefan Johansen.
76:23 SubstitutionSubstitution Substitution, Celtic. Tyler Blackett replaces Kieran Tierney.
73:50 SubstitutionSubstitution Substitution, Celtic. Tomas Rogic replaces Kris Commons.
72:12William Gibson (Stranraer) wins a free kick in the defensive half.
72:12Foul by Stefan Johansen (Celtic).
68:15 SubstitutionSubstitution Substitution, Celtic. Scott Allan replaces Carlton Cole.
Attempt missed. Kris Commons (Celtic) left footed shot from outside the box is close, but misses to the right.
67:00Corner, Celtic. Conceded by Max Currie.
66:52Attempt saved. Leigh Griffiths (Celtic) right footed shot from the left side of the box is saved in the top right corner.
61:45Paul Cairney (Stranraer) wins a free kick in the attacking half.
61:45Foul by Stefan Johansen (Celtic).
60:32 SubstitutionSubstitution Substitution, Stranraer. William Gibson replaces Sam McCloskey.
60:06 SubstitutionSubstitution Substitution, Stranraer. Andy Stirling replaces Mark McGuigan.
58:39Foul by Scott Robertson (Stranraer).
58:39Kris Commons (Celtic) wins a free kick in the attacking half.
57:27Attempt saved. Leigh Griffiths (Celtic) left footed shot from outside the box is saved in the top centre of the goal.
50:54Attempt saved. Carlton Cole (Celtic) right footed shot from the centre of the box is saved in the bottom right corner.
48:30Steven Bell (Stranraer) wins a free kick in the defensive half.
48:30Foul by Leigh Griffiths (Celtic).
47:42Attempt saved. Kris Commons (Celtic) left footed shot from the centre of the box is saved in the bottom left corner.
45:00Second Half begins Stranraer 0, Celtic 2.
45:00 +0:08 Half timeHalf Time First Half ends, Stranraer 0, Celtic 2.
41:41 Goal scoredGoal! Goal! Stranraer 0, Celtic 2. Carlton Cole (Celtic) header from the left side of the six yard box to the bottom left corner. Assisted by Nir Bitton.
40:37Attempt saved. Leigh Griffiths (Celtic) left footed shot from the right side of the box is saved in the bottom right corner.
39:53Scott Robertson (Stranraer) wins a free kick in the defensive half.
39:53Foul by Carlton Cole (Celtic).
36:41Scott Rumsby (Stranraer) wins a free kick in the attacking half.
36:41Foul by Carlton Cole (Celtic).
35:52Corner, Celtic. Conceded by Max Currie.
35:42Attempt saved. Kris Commons (Celtic) left footed shot from the right side of the box is saved in the top right corner.
33:37Foul by Paul Cairney (Stranraer).
33:37Nir Bitton (Celtic) wins a free kick in the attacking half.
31:57Corner, Celtic. Conceded by Craig Pettigrew.
29:13Jamie Longworth (Stranraer) wins a free kick in the attacking half.
29:13Foul by Stefan Johansen (Celtic).
24:23Attempt missed. Leigh Griffiths (Celtic) left footed shot from outside the box is close, but misses the top right corner.
21:31Attempt missed. Craig Malcolm (Stranraer) right footed shot from the centre of the box is close, but misses to the right.
21:00Steven Bell (Stranraer) wins a free kick on the right wing.
20:58Foul by Kris Commons (Celtic).
17:45 Goal scoredGoal! Goal! Stranraer 0, Celtic 1. Leigh Griffiths (Celtic) left footed shot from the centre of the box to the bottom right corner. Assisted by Callum McGregor.
14:22Scott Robertson (Stranraer) wins a free kick in the attacking half.
14:22Foul by Carlton Cole (Celtic).
13:56Foul by Scott Robertson (Stranraer).
13:56Mikael Lustig (Celtic) wins a free kick in the defensive half.
8:52Corner, Celtic. Conceded by Scott Robertson.
4:00Mikael Lustig (Celtic) wins a free kick in the defensive half.
3:58Foul by Sam McCloskey (Stranraer).
0:00First Half begins.
0:00Lineups are announced and players are warming up.
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